In fluid-friction couplings of the kind referred to above, the valve arm controls the flow of fluid from the reservoir into the work space. The valve arm is controlled on the one hand by a bimetal mounted outside of the coupling housing (a so-called external bimetal) and, on the other hand, by a further bimetal mounted within the reservoir of the coupling (a so-called internal bimetal). The internal bimetal is attached to the partition wall between the reservoir and the work chamber and operates on the valve arm in the closure direction when a specific limit temperature is reached so that the valve arm closes the valve port and shuts the coupling. In this way, an overheating of the fluid, that is the viscous silicone oil, is avoided. It is disadvantageous in this arrangement that the valve port is not positively closed exclusively by the actuation of the inner bimetal so that the fan speed then drops to an undetermined value. Accordingly, this coupling tends to chatter.